I did some more research and Iridium can provide a location based on the "spot beam" -- it uses directional antennae for terrestrial communication so the system knows which "spot" a user is in. However, the spot beam is 250mi in diameter. As the satellites move a ground station will move out of one spot and into another, so it's safe to assume that the location data will be more precise than that over time.

What I still don't know is if the satellite software allows for Doppler triangulation like Russ suggests.